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 A173280 First column of the matrix power A173279(.,.)^j in the limit j->infinity. 3
 1, 1, 3, 7, 29, 129, 757, 5185, 41155, 368351, 3671635, 40295943, 482758111, 6268066531, 87668492115, 1314023850727, 21011431917453, 357014074280785, 6423561495057421, 122004755658629081, 2439367774898883497, 51213663674167659301, 1126452985959434543237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS We can generalize A173279 to other matrices derived from some sequence S by Smat(n,k) := S(n-r*k), r >= 2, and find that they define sequences B(x) via S(x)= B(X)/B(x^r), b(n) = Sum_{t=0..n, n-t == 0 (mod r)} S(t)*B_{(n-t)/r}. The sequence here is the case of S=A000142 and r=2. LINKS FORMULA A000142(x) = A(x)/A(x^2), where A(x) and A000142(x) are the o.g.f.'s associated with A000142 and this sequence here. Sum_{n>=0} 1/a(n) = 2.519966353393413186683398448854995831308... a(n) = (A173279^j)(n,0). a(n) = Sum_{t=0..n, n-t even} t!*a_{(n-t)/2}. - R. J. Mathar, Feb 22 2010 MAPLE A173280 := proc(n) option remember; local a, l; if n = 0 then 1; else a :=0 ; for l from n to 0 by -2 do a := a+ l!*procname((n-l)/2) : end do ; a ; end if; end proc: seq(A173280(n), n=0..60) ; # R. J. Mathar, Feb 22 2010 CROSSREFS Cf. A000142. Sequence in context: A358389 A358279 A217576 * A141477 A211371 A302157 Adjacent sequences: A173277 A173278 A173279 * A173281 A173282 A173283 KEYWORD nonn AUTHOR Gary W. Adamson, Feb 14 2010 EXTENSIONS Extended, and invalid comment on convergence to e removed, by R. J. Mathar, Feb 22 2010 Index of B in the convolution formula in the comment corrected by R. J. Mathar, Mar 23 2010 STATUS approved

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Last modified December 5 05:50 EST 2022. Contains 358578 sequences. (Running on oeis4.)